Question: Simplify. Rewrite the expression in the form $2^n$. $2^3\cdot 2^7=$
$\begin{aligned} 2^3\cdot 2^7&=2^{3+7} \\\\ &=2^{10} \end{aligned}$ This follows from the general rule $x^m\cdot x^n=x^{m+n}$. Note that the powers have the same base. We can also see this is correct by expanding the powers. $\begin{aligned} 2^3\cdot 2^7&=\underbrace{2\cdot 2\cdot 2}_\text{3 times}\cdot\underbrace{2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2}_\text{7 times} \\\\\\ &=\underbrace{2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2\cdot 2}_\text{10 times} \\\\ &=2^{10} \end{aligned}$ In conclusion, $2^3\cdot 2^7=2^{10}$.